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In this paper, We apply A Hopfield neural network dynamic model with an improved energy function to edge detection of log digital images. The edge detection problem in this paper was formulated as an optimization process that sought the edge points to minimize an energy function which is different from the traditional methods. The dynamics of Hopfield neural networks were applied to solve the optimization problem. An initial edge was first estimated by the method of traditional edge algorithm. The gray value of image pixel was described as the neuron state of Hopfield neural network. The state updated till the energy function touch the minimum value. The final states of neurons were the result image of edge detection. The novel energy function ensured that the network converged and reached a near-optimal solution. Taking advantage of the collective computational ability and energy convergence capability of the Hopfield network, the noises will be effectively removed. The experimental results showed that our method can obtain more vivid and more accurate edge than using the traditional methods.